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Results for “singularities in general relativity”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Lateral control system design for VTOL landing on a DD963 in high sea states

The problem of designing lateral control systems for the safe landing of VTOL aircraft on small ships is addressed. A ship model is derived. The issues of estimation and prediction of ship motions are discussed, using optimal linear linear estimation techniques. The roll motion is the most important of the lateral motions, and it is found that it can be predicted for up to 10 seconds in perfect conditions. The automatic landing of the VTOL aircraft is considered, and a lateral controller, defined as a ship motion tracker, is designed, using optimal control techniqes. The tradeoffs between the tracking errors and the control authority are obtained. The important couplings between the lateral motions and controls are demonstrated, and it is shown that the adverse couplings between the sway and the roll motion at the landing pad are significant constraints in the tracking of the lateral ship motions. The robustness of the control system, including the optimal estimator, is studied, using the singular values analysis. Through a robustification procedure, a robust control system is obtained, and the usefulness of the singular values to define stability margins that take into account general types of unstructured modelling errors is demonstrated. The minimal destabilizing perturbations indicated by the singular values analysis are interpreted and related to the multivariable Nyquist diagrams.

Bodson, M.↗
NASA NTRS1995

Computing supernova collapse to neutron stars and black holes

We present a new numerical code for spherical hydrodynamics in general relativity. The code can handle gravitational collapse to a neutron star or to a black hole without the appearance of singularities. Moreover, the variables and equations in the code are very similar to those appearing in traditional Lagrangian supernova codes. Any such existing code can thus be easily adapted to treat collapse where the final fate is uncertain and may be either a neutron star or a black hole. The code is based on the formulation of Hernandez & Misner, in which retarded time is used as coordinate. This prevents the computational grid from penetrating inside any black hole that may form. We present the equations and a complete finite difference scheme for the adiabatic evolution of a fluid that obeys a gamma-law equation of state. We summarize the results of several testbed calculations performed to check our code. We also give the transformation of the analytic Oppenheimer-Snyder solution for homogeneous dust collapse to our coordinate system.

Baumgarte, Thomas W.↗
DOE OSTI2026

Causal horizons, geodesic completeness and stability in slow contraction cosmology

We show that cosmological models with a semi-infinite phase of slow contraction (ekpyrosis) possess a combination of properties that can address several fundamental problems in cosmology, otherwise faced in contracting de Sitter phases or standard big bang expansion. In particular, flat or open slow contraction admits a stable past attractor that asymptotes to Minkowski space and is past geodesically complete, as well as a stable, flat, homogeneous, and isotropic future attractor with negligible Weyl curvature (and, therefore, negligible gravitational entropy). In bouncing cosmologies, this contracting attractor is terminated by a smooth, non-singular bounce that transforms the attractor properties at the end of contraction into the initial conditions for the subsequent expanding phase. Cosmologies incorporating a slow contraction phase have no particle horizon and therefore avoid the causal horizon problem. The past Minkowski attractor also generates an initial spectrum of vacuum-like quantum fluctuations on all wavelengths. Moreover, because the averaged expansion rate along past-directed geodesics is non-positive, models incorporating a semi-infinite phase of slow contraction also evade the Borde–Guth–Vilenkin theorem. By contrast, contracting de Sitter space possesses a finite particle horizon and becomes unstable in the presence of scalar fields, matter, or radiation.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗
NASA NTRS1977

Unsteady supersonic aerodynamic theory for interfering surfaces by the method of potential gradient

A generalized solution of the hyperbolic wave equation was further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals were evaluated in closed form, with numerical integration methods for more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient. Streamwise integrals were performed analytically, and spanwise integrals were neccessary only on element leading and trailing sides. All integrands vanish on the Mach cone. Pressure distribution on a double delta wing and generalized aerodynamic coefficients for three AGARD planforms were calculated and compared with available results.

Jones, W. P.↗
DOE OSTI2024

Ladder symmetries and Love numbers of Reissner-Nordström black holes

It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner-Nordström black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1982

A cylindrical shell with an arbitrarily oriented crack

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system of five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented.

Yahsi, O. S.↗
NASA NTRS1983

A cylindrical shell with an arbitrarily oriented crack

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system to five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented. Previously annunced in STAR as N83-16783

Yahsi, O. S.↗
DOE OSTI2024

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS 3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

Unsteady supersonic aerodynamic theory by the method of potential gradient

A generalized solution of the hyperbolic wave equation has been derived. The method used has been further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals have been evaluated in closed form, while numerical integration methods are suggested for treating more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient because line integrations along the other two sides need only be considered. Furthermore, all the integrands vanish on the Mach cone and the need for determining the hyperbolic curves of intersection of the cone with the lifting surface is avoided. Generalized aerodynamic coefficients for three AGARD planforms have been calculated and compared with the available results.

Jones, W. P.↗
DOE OSTI2021

Constraints on a massive double-copy and applications to massive gravity

We propose and study a BCJ double-copy of massive particles, showing that it is equivalent to a KLT formula with a kernel given by the inverse of a matrix of massive bi-adjoint scalar amplitudes. For models with a uniform non-zero mass spectrum we demonstrate that the resulting double-copy factors on physical poles and that up to at least 5-particle scattering, color-kinematics duality satisfying numerators always exist. For the scattering of 5 or more particles, the procedure generically introduces spurious singularities that must be cancelled by imposing additional constraints. When massive particles are present, color-kinematics duality is not enough to guarantee a physical double-copy. As an example, we apply the formalism to massive Yang-Mills and show that up to 4-particle scattering the double-copy construction generates physical amplitudes of a model of dRGT massive gravity coupled to a dilaton and a two-form with dilaton parity violating couplings. We show that the spurious singularities in the 5-particle double-copy do not cancel in this example, and the construction fails to generate physically sensible amplitudes. We conjecture sufficient constraints on the mass spectrum, which in addition to massive BCJ relations, guarantee the absence of spurious singularities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Collisions of localized shocks and quantum circuits

We study collisions between localized shockwaves inside a black hole interior. We give a holographic boundary description of this process in terms of the overlap of two growing perturbations in a shared quantum circuit. The perturbations grow both exponentially as well as ballistically. Due to a competition between different physical effects, the circuit analysis shows dependence on the transverse locations and exhibits four regimes of qualitatively different behaviors. On the gravity side we study properties of the post-collision geometry, using exact calculations in simple setups and estimations in more general circumstances. We show that the circuit analysis offers intuitive and surprisingly accurate predictions about gravity computations involving non-linear features of general relativity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1996

On the Stochastic Quantization Method: Characteristics and Applications to Singular Systems

Introducing the generalized Langevin equation, we extend the stochastic quantization method so as to deal with singular dynamical systems beyond the ordinary territory of quantum mechanics. We also show how the uncertainty relation is built up to the quantum mechanical limit with respect to fictitious time, irrespective of its initial value, within the framework of the usual stochastic quantization method.

Kanenaga, Masahiko↗
DOE OSTI2022

Radiative properties of an artificial atom coupled to a Josephson-junction array

We study the radiative properties—the Lamb shift, Purcell decay rate, and spontaneous emission dynamics—of an artificial atom coupled to a long, multimode cavity formed by an array of Josephson junctions. Introducing a tunable coupling element between the atom and the array, we demonstrate that such a system can exhibit a crossover from a perturbative to a nonperturbative regime of light-matter interaction as one strengthens the coupling between the atom and the Josephson-junction array. As a consequence, the concept of spontaneous emission as the occupation of the local atomic site being governed by a single complex-valued exponent breaks down. This breakdown, we show, can be interpreted in terms of formation of hybrid atom-resonator modes with radiative losses that are nontrivially related to the effective coupling between individual modes. We develop a singular function expansion approach for the description of the open quantum system dynamics in such a multimode nonperturbative regime. This modal framework generalizes the normal-mode description of quantum fields in a finite volume, incorporating exact radiative losses and incident quantum noise at the delimiting surface. Our results are pertinent to recent experiments with Josephson atoms coupled to high-impedance Josephson-junction arrays.

42 ENGINEERING↗
NASA NTRS1977

Pure field theories and MACSYMA algorithms

A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.

Ament, W. S.↗
NASA NTRS2023

Relationship Between the Sub-Micron Fraction (SMF) and Fine-Mode Fraction (FMF) in the Context of AERONET Retrievals

The sub-micron (SM) aerosol optical depth (AOD) is an optical separation based on the fraction of particles below a specified cutoff radius of the particle size distribution (PSD) at a given particle radius. It is fundamentally different from spectrally separated FM (fine-mode) AOD. We present a simple (AOD-normalized) SM fraction versus FM fraction (SMF vs. FMF) linear equation that explains the well-recognized empirical result of SMF generally being greater than the FMF. The AERONET inversion (AERinv) products (combined inputs of spectral AOD and sky radiance) and the spectral deconvolution algorithm (SDA) products (input of AOD spectra) enable, respectively, an empirical SMF vs. FMF comparison at similar (columnar) remote sensing scales across a variety of aerosol types. SMF (AERinv-derived) vs. FMF (SDA-derived) behavior is primarily dependent on the relative truncated portion (ε c ) of the coarse-mode (CM) AOD associated with the cutoff portion of the CM PSD and, to a second order, the cutoff FM PSD and FM AOD (ε f ). The SMF vs. FMF equation largely explains the SMF vs. FMF behavior of the AERinv vs. SDA products as a function of PSD cutoff radius (“inflection point”) across an ensemble of AERONET sites and aerosol types (urban-industrial, biomass burning, dust, maritime and a mixed class of Arctic aerosols). The overarching dynamic was that the linear SMF vs. FMF relation pivots clockwise about the approximate (SMF, FMF) singularity of (1, 1) in a “linearly inverse” fashion (slope and intercept of approximately 1−ε c and ε c ) with increasing cutoff radius. SMF vs. FMF slopes and intercepts derived from AERinv and SDA retrievals confirmed the general domination of ε c over ε f in controlling that dynamic. A more general conclusion is the apparent confirmation that the optical impact of truncating modal (whole) PSD features can be detected by an SMF vs. FMF analysis.

Norman T. O'Neill↗